21. Use the figures to answer the following questions. You should explain how yo
ID: 1457666 • Letter: 2
Question
21. Use the figures to answer the following questions. You should explain how you determine the directions of any vectors requested. a. The current in the wire is 2.0 A and r = 1.5 cm. An electron is moving with velocity 9 x 10^5 m/s in the direction indicated. Determine the magnitude and direction of the magnetic force that the electron experiences. b. The figure shows a loop of current. A proton is traveling so that it passes the center of the loop. At that location, its velocity is directed into the page. What is the direction of the magnetic force that the current loop exerts on the proton? c. The magnetic field at Point P is zero. In what direction is the current flowing through the unlabeled wire? What is the direction of the magnetic force that each wire exerts on the other wire?Explanation / Answer
(a) Let positive x and y directions be right and up respectively.
B = µoI/2r = (4 * 10-7) * 2 / (2 * 0.015) = 2.67 * 10-5 T (directed into the page)
v = 9 * 105 m/s
B is perpendicular to v.
Magnitude of force on the electron, F = qvB = (1.6 * 10-19)(9 * 105)(2.67 * 10-5) = 3.8 * 10-18 N
This force lies in the plane of the paper and makes an angle of 150o with the positive x-axis.
(b) Magnetic field at the centre of loop, B = µoI/2R
This magnetic field is directed out of the page and perpendicular to it.
F = q(v x B)
Since the angle between v and B is 180o, v x B = 0
Hence, F = 0
(c) Magnetic field due to the first wire at P is into the page. So, magnetic field due to the second wire at P needs to be out of the page. Hence, current in the second wire should be upward.
Force between wires, F = I(L x B)
Hence, it can be seen that force on right wire is towards left and force on left wire is towards right. The wires attract each other.
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